Max Euwe and chess - how did he use mathematics to get ahead?

I don't really know what you're talking about regarding Alekhine...since it was widely thought to be a fluke when Euwe beat him in 1935 (and the 1937 rematch went convincingly in Alekhine's favor). I suppose you could say the answer to your question is "yes," since computers more or less use math to play the game, and they're pretty damned good...but for humans it's more complicated. Some great players (Anderssen, Euwe, Emanuel Lasker, just to name the ones I can think of) were gifted at math; others--in fact, most others--were not particularly so. Actually (so they say) musical talent is a far more common feature of great players. (And sorry, William B, but as your link in fact says, Euwe was a math professor--not a doctor.)